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A213930 Table of frequencies of gaps of size 2d between consecutive primes below 10^n, n >= 1; d = 1,2,...,A213949(n).

%I A213930 #27 May 01 2013 10:27:36
%S A213930 2,8,7,7,1,35,40,44,15,16,7,7,0,1,1,205,202,299,101,119,105,54,33,40,
%T A213930 15,16,15,3,5,11,1,2,1,1224,1215,1940,773,916,964,484,339,514,238,223,
%U A213930 206,88,98,146,32,33,54,19,28,19,5,4,3,5
%N A213930 Table of frequencies of gaps of size 2d between consecutive primes below 10^n, n >= 1; d = 1,2,...,A213949(n).
%C A213930 Sum of elements in line n is Pi(10^n)-2. Column d is the sequence of the numbers of gaps of size 2d between consecutive primes up to 10^n. For example, column 1 is A007508, and column 2 is A093737. Column 3 corresponds to the jumping champion 6. Column 15 corresponds to the next champion 30. It is interesting that local maximums appear in the beginning of this column, 11 in line 4, and 146 in line 5.
%H A213930 Washington Bomfim, <a href="/A213930/b213930.txt">Rows n = 1..13, flattened</a>
%H A213930 A. Odlyzko, M. Rubinstein and M. Wolf, <a href="http://www.dtc.umn.edu/~odlyzko/doc/jumping.champions.pdf">Jumping Champions</a>
%H A213930 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%e A213930 Table begins
%e A213930    2
%e A213930    8    7    7   1
%e A213930   35   40   44  15  16   7   7   0   1   1
%e A213930   205  202  299 101 119 105  54  33  40  15  16  15  3  5  11  1  2  1
%e A213930 1224 1215 1940 773 916 964 484 339 514 238 223 206 88 98 146 32 33 54 19 28...
%t A213930 Table[t2 = Sort[Tally[Table[Prime[k + 1] - Prime[k], {k, 2, PrimePi[10^n] - 1}]]]; maxDiff = t2[[-1, 1]]/2; t3 = Table[0, {k, maxDiff}];Do[t3[[t2[[i, 1]]/2]] = t2[[i, 2]], {i, Length[t2]}]; t3, {n, 5}] (* _T. D. Noe_, Jun 25 2012 *)
%Y A213930 Cf. A038460, A000720, A007508, A093737, A213949 (row lengths).
%K A213930 tabf,nonn,nice
%O A213930 1,1
%A A213930 _Washington Bomfim_, Jun 24 2012